I assume you are trying this on the survey123.esri.com website as opposed to AGO? If so, we have been having the same problem. For us it has worked a few times, but not consistently. Deleting internet temp files seems to help as does waiting a min. or so once the panel to select groups opens before clicking anything. Is that crazy or what? Older surveys seem to have more issues than new ones for us. Also Chrome seem much more likely to display the group selection panel than IE11. Hopping on one foot may also help but we still need to do some testing with that method.